Washington (CNN) - The top Democrat in the House is pushing back against calls to extend open enrollment in the new health care exchanges because of the massive technical problems plaguing HealthCare.gov.

"I don't support that," House Minority Leader Nancy Pelosi said Wednesday morning, just hours after Sen. Jeanne Shaheen of New Hampshire appeared to be the first Democrat in Congress to join a growing number of her Republican colleagues in suggesting the deadline be pushed back.